Abstract
We construct a (bi)cyclic sieving phenomenon on the union of dominant maximal weights for level ℓ highest weight modules over an affine Kac-Moody algebra with exactly one highest weight being taken for each equivalence class, in a way not depending on types, ranks and levels. In order to do that, we introduce S-evaluation on the set of dominant maximal weights for each highest modules, and generalize Sagan's action in [17] by considering the datum on each affine Kac-Moody algebra. As consequences, we obtain closed and recursive formulae for cardinality of the number of dominant maximal weights for every highest weight module and observe level-rank duality on the cardinalities.
| Original language | English |
|---|---|
| Article number | 107336 |
| Journal | Advances in Mathematics |
| Volume | 374 |
| DOIs | |
| State | Published - 18 Nov 2020 |
Bibliographical note
Funding Information:The research of Y.-H. Kim was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (NRF-2018R1D1A1B07051048).S.-j. Oh was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019R1A2C4069647).The research of Y.-T. Oh was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (NRF-2018R1D1A1B07051048).
Publisher Copyright:
© 2020 Elsevier Inc.
Keywords
- Affine Kac-Moody algebra
- Cyclic sieving phenomenon
- Dominant maximal weight